ON THE METRIC AND THE TOPOLOGICAL PROPERTIES OF THE CONVERGENCE FIELD OF REGULAR MATRIX TRANSFORMATIONS

Abstract

It has been shown by some researchers that the convergence field of regular matrix transformation is a very porous set in the spaceof all sequence of real or complex numbers while in [11 ], it have been proven to be σ-porous set in the linear metric space endowed with Fréchet metric. Also, the usefulness of the well-known theorem on discontinuity points of function of the first bare class has been presented. Thus in this paper, we proved that the convergence field of a various matrix transformation is a metric space as well as a topological space. Further, we have shown that the space is normal and first countable; compact and complete and have unique fix point.